Authors: Dragović, Vladimir 
Radnović, Milena
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Periods of Pseudo-Integrable Billiards
Journal: Arnold Mathematical Journal
Volume: 1
Issue: 1
First page: 69
Last page: 73
Issue Date: 1-Mar-2015
ISSN: 2199-6792
DOI: 10.1007/s40598-014-0004-0
Abstract: 
Consider billiard desks composed of two concentric half-circles connected with two edges. We examine billiard trajectories having a fixed circle concentric with the boundary semicircles as the caustic, such that the rotation numbers with respect to the half-circles are ρ1 and ρ2 respectively. Are such billiard trajectories periodic, and what are all possible periods for given ρ1 and ρ2?.
Keywords: Billiards | Concentric circles | Periodic trajectories | Rotation numbers
Publisher: Springer Link
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 
Australian Research Council, Grant no. FL120100094

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